Mathematically Calculated Low Tier Tournament Character Rankings (Update w Tier List)

First of all the inspiration for this thread was Wesley's thread. for mathematically calculating a tier list based on Phanna's matchup chart. See this thread for the basic premise, mathematical explanations, etc.

"But we already have low tier rankings!"

Yes, but if you consider only matchups between low tiers the rankings are quite different.

Assuming an initially even distribution of low tier characters in low tier tournaments, the rankings are

1) Ness : 6.285714285714286------19.3044549705395
2) Pikachu : 5.714285714285714------11.271079197600537
3) Y. Link : 5.642857142857143------10.53789813239882
4) Link : 5.5------9.211513337141515
5) Yoshi : 5.428571428571428------8.612306549375957
6) Mr. G&W : 5.357142857142857------8.052078022984318
7) Luigi : 5.285714285714286------7.528292231182244
8) Zelda : 4.999999999999998------5.752418144841862
9) DK : 4.928571428571429------5.378224690161977
10) Roy : 4.928571428571429------5.378224690161977
11) Mewtwo : 4.285714285714286------2.9358603495706523
12) Kirby : 4.0------2.24331041184089
13) Bowser : 3.8571428571428568------1.9609492821427412
14) Pichu : 3.785714285714285------1.8333899900570236

The left number indicates a character's "power level," a kind of "absolute" ranking. Strictly speaking, it's the expected Phanna matchup average against randomly selected characters given the constraints of the character populations. The number on the right predicts the distribution of characters (as a percentage) in low tier tourneys, assuming the distribution follows a similar pattern as for regular tourneys, which it may not. If redistribution in subsequent tourneys follows in a similar fashion, then for a large number of iterations we get the following stable rankings:



As you can see these rankings are significantly different from those in the regular tier list. I hope this gives some kind of idea of character potential in low-tier tourneys.

NOTE: These rankings assume the accuracy of the Phanna chart. Don't tell me Ness is higher than he should be. He probably is, but voice your concerns in Phanna's thread. Also, the formula used for predicting player redistribution is inherently arbitrary. My only goal was to get a good spread, where more players use higher ranked characters than lower ranked characters. However, this kind of model may not be accurate for low tier tourneys, as character decisions are probably focused less on maximizing win potential and more on other elements like "fun" than in regular tourneys.

Edit: As you can see from the image, some of the power levels are quite close to each other meaning their ordering is not very meaningful. We could break the list into tiers as follows:

God Tier
1) Ness

Top Tier
2) Pikachu

High Tier
3) Yoshi
4) Y. Link
5) Link
6) Mr. G&W
7) Luigi

Middle Tier
8) Zelda
9) DK

Low Tier
10) Roy
11) Kirby
12) Mewtwo

Bottom Tier
13) Bowser
14) Pichu

Six tiers is probably overkill for 14 characters, but this is where the clear boundaries between power levels are. Rankings within tiers are less significant than the rankings of the tiers.

Wow, this is impressive. Good work, Shai.

Great job. Are you using the same formula as wesley?? I just wanna make sure I know the math behind it.

GJ on this.... It'd be funny If one character's was 3.14159265358979!

I feel like Luigi should be higher; I'll probably look at some of the chart match-ups for him more closely during the next update.

Also, just as a general comment to these lists - is 15 significant digits really necessary? _X.XX should be plenty, and look less clutterered..

ZOMG... the Ness boards were right!

ZOMG X2... the Roy boards were right!

people talk on the roy boards???? i thought that they were about to be renamed the spam boards

phanna said:

I feel like Luigi should be higher; I'll probably look at some of the chart match-ups for him more closely during the next update.

Also, just as a general comment to these lists - is 15 significant digits really necessary? _X.XX should be plenty, and look less clutterered..

Click to expand...

Lol yeah, but it's been a couple years since I had any programming classes and I forgot how to format the numbers. I'm using Java. I'll look it up and repost neater lists.

My power formula is the same as Wesley's, except I use a fraction of character users instead of absolute population. Simpler that way, I think.

Pi = Sigma from j = 13 to 26 (Mj * Fj)

Pi = power of character
Mj = matchup against jth character
Fj = fraction using jth character

or in code:

for (int j = 13; j<=26; j++) {
list.setPower(list.getPower() + match[j] * list[j].getFraction());
}

My redistribution formula is different but it's probably similar. The redistribution is inherently arbitrary and the only real goal is to get a good spread that stabilizes over many iterations.

F = A^(B * P / S)

A = alpha, an arbitrary constant
B = beta, an arbitrary constant
S = sum of all powers

Then I just made the values of alpha and beta such that they gave a satisfactory spread.

In code:

list.setFraction(Math.pow(alpha, beta * list.getPower() / sum));

You may notice that this F I'm calculating isn't really the true fraction as the sum will exceed 1. So each iteration I scale the fractions down by dividing over the sum of the fractions.

Edit: Thanks Phanna

Shai Hulud said:

I posted a neater chart but I can't do images so there's just a link. Someone who can post images can repost it in here if you want.

Click to expand...

All you have to do is put the URL of where you uploaded it between tags, like this:



fake edit: You also have to take off any arguments, in this case, the "?t=1176154157" at the end of the URL

****IT! STOP EXPOSING THE GREATNESS OF NESS!

*we mussst hides it!*

Lol cool thread I love low tiers, however the least played character is DK i think and right near there is bowser and M2 even in low tier games, I think you end up with alot of Link and for some reason Luigi is alot better played at a pro level than I thought possible, so any character that has a natural advantage vs those two characters are going to due better in a low tier tournament, then again that doesnt take into account other variables like who they are weak against. I like it though, and it does make sense, and you did already point out what I am saying now, just the ness threads link this as a valid argument for playing him.

Luigi will always **** low tier tourneys.

Rob_Gambino said:

Luigi will always **** low tier tourneys.

Click to expand...

Yeah, this may be an indication that some of the low tier matchup values are a bit off...

WHAT DOES THE SCOUTER SAY ABOUT PICHU'S POWER LEVEL?!?!

IIIITTT'SSSS OOOVVVERRRR THHHREEEEE POOINT TTTWWWWEEEELLLLVVVVVEEE!!!!!!!!!!!!!!!!

Yes, well, anyway, I suppose that's impressive, but what about distance? We've got people who can send people flying yet doesn't do much damage. Since this game doesn't use HP, the object of the game is to ultimately get people off the edge, and if it's any consellation, I've noticed more people try the said stragety as opposed to just weakening them.

Well, meh, maybe, since it's low tiers were dealing with here, it could be a slightly bigger deal.